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Solving First Degree Equations

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First Degree Equation: An equation characterized by having a single variable
... which may be repeated within the equation more than once ... which
is raised to the first power. Note: plain variable "x" is the same as "x^{1}"
... plain variable "x" is the same as "x" raised to the first power.

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A typical 1st degree equation is shown below ... together with the normal
steps of solutions:

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STEP 1: __Eliminate parenthesis__ (if any) by multiplying through
using the distributive property.

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STEP 2: __Eliminate fractions__ (if any) by finding the common
denominator and multiplying the entire equation through by the common denominator.
In this example, "12" is the common denominator. NOTE: Notice that the
negative sign in front of the compound fraction "(5x - 3)/4" must be distributed
through the entire numerator. You are subtracting the total fraction.

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STEP 3: __Combine like terms __(if any) on both the left and right sides
of the equation.

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STEP 4: __Isolate "x"__ (or the variable being solved for) __to
one side __of the equation ... and at the same time get non-"x" terms
to the opposite side. In this example, you'd subtract "10x" from both sides
of the equation (add "-10x" to both sides) ... and subtract "7" from both
sides of the equation.

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STEP 5: __Get "x" by its lonesome__ (get the variable all by itself).
In this example, divide both sides of the equation by "5" (or, equivalent,
multiply both sides of the equation by the fraction "1/5".

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STEP 6 (optional): Once an answer is produced, it should be able to be
substituted into the original equation ... and make it true. This is a
method that can be used to "check" an answer.

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